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Polynomial

Total questions: 33

Worksheet time: 6hrs 29mins

Name
Class
Date
1.
(2x3 + 7x2 - 6x - 8) ÷ (x+ 4)
a)
2x2 - x - 2
b)
2x3 - x2 - 2x
c)
2x2 + 15x + 54 + 208/x+4
d)
2x3 + 15x2 + 54x + 208
2.

Divide the polynomial.

a)

2x2 + 3x + 8 + -57/x-4

b)

2x2 - 13x - 56

c)

2x2 + 3x + 8 +7/x-4

d)

2x2 - 3x - 16 + -89/x-4

3.
a)
This is correct
b)
This is incorrect
4.

(x3-8x2+6x+41)÷(x-4)

a)

x2-4x-7, R 2

b)

x2-4x-11, R 1

c)

x2-2x-12, R 3

d)

x2-4x-10, R 1

5.
What should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)
a)
3   0   -4   6   1
b)
6   -4   3   1   0
c)
6   -4   0   3   1
d)
-6   4   0   -3   -1
6.

(27x3 + 9x2 - 3x - 10) ÷ (3x - 2)

a)

9x4+5

b)

9x2+9x+5

c)

9x2-9x+5

d)

9x2-9x

7.

Which of the following would be a root with 3i?

a)

3i2

b)

-3i

c)

3i

d)

-3i2

8.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

9.

Write the polynomial with the given zeros

a)

A

b)

B

c)

C

d)

D

10.
How many roots or zeros does the equation
f(x) = 5x4-8x3+4x2-6x+3 have?
a)
3
b)
4
c)
5
d)
0
11.
Classify the function:
a)
quadratic
b)
cubic 
c)
quartic
d)
linear
12.
Find all zeros of the polynomial function P(x) = x3+6x2+9x+54
a)
6, 3, -3
b)
-6, 3, -3
c)
-6, 3i, -3i
d)
6, 3i, -3i
13.
Is (x-3) a factor of
(x3 - 3x2 + 2x + 2)?
a)
Yes
b)
No
14.
Is (x-7) a factor of (x2-5x+14)?
a)
Yes
b)
No
15.
If 𝒙2−𝟓 is divided by 𝒙−𝟐, then what is the remainder?
a)
1
b)
-1
c)
9
d)
0
16.
Use Synthetic Substitution to find f(-2)
f(x) = 2x4 - 3x3 + 1
a)
A.  f(-2) = 51
b)
B.  f(-2) = 11
c)
C.  f(-2) = 63
d)
D.  f(-2) = 57
17.
Find all the factors of   x3 -3x2 -4x +12 given that -2 is a zero.
a)
(x-2) (x+2) (x+3) 
b)
(x-2) (x-2) (x+3)
c)
(x+2) (x+2) (x+3)
d)
(x-2) (x+2) (x-3)
18.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
19.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
20.
What is the degree of the polynomial?
a)
2
b)
3
c)
4
d)
5
21.
How many roots or zeros does the equation
f(x) = 5x4-8x3+4x2-6x+3 have?
a)
3
b)
4
c)
5
d)
0
22.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
23.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
24.

What is the degree and leading coefficient?

a)

Degree- odd

Leading coefficient- positive

b)

Degree- odd

Leading coefficient- negative

c)

Degree- even

Leading coefficient- positive

d)

Degree- even

Leading coefficient- negative

25.

What is a possible multiplicity of the zero -1?

a)

Multiplicity 1

b)

Multiplicity 2

c)

Multiplicity 3

26.
Classify this polynomial by its degree and number of terms:  x2 + 6
a)
Linear polynomial
b)
Quadratic trinomial
c)
Quadratic binomial
d)
Cubic binomial
27.
Classify this polynomial by its degree and number of terms:  x2 + 2x3 + 6
a)
Cubic polynomial
b)
Quadratic binomial
c)
Quadratic trinomial
d)
Cubic trinomial
28.

8

a)

Constant polynomial

b)

Linear monomial

c)

Constant monomial

d)

Linear monomial with 0 terms

29.

9x4

a)

Quadratic polynomial

b)

Quartic monomial

c)

Quadratic monomial

d)

Cubic monomial

30.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
31.
Find the difference. 
(3- 2x + 2x2) - (4x -5 +3x2)
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
32.
Multiply
(4x+3)(2x-1)
a)
8x2-2x-3
b)
8x-3
c)
8x2+6x-3
d)
8x2+2x-3
33.
Multiply
x2(2x+3)
a)
x2+2x+3
b)
2x+3
c)
2x2+3x
d)
2x3+3x2

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